This invention relates to a method for shaping the input to a dynamic system in order to minimize unwanted dynamics in that system.
Many physical systems must operate dynamically in order to accomplish their intended functions. However, in the course of their motions, the systems may acquire unwanted dynamics and vibrations which may be detrimental to their operation. For example, excessive vibrations in a dynamic system may result in larger than normal stresses and a premature failure of that system. Alternatively, if the system is designed to operate with a smooth, non-oscillatory motion, then vibrations may cause unwanted oscillations which actually prevent the system from achieving its intended purpose, or, at the very least, cause the system to operate at a significantly slower speed and lower performance level than originally intended. In addition, the unwanted dynamics may also degrade the performance of the system, either directly or indirectly, since the system is not exactly following its intended motion. As a result of these consequences, it is often desired to minimize the unwanted dynamics and vibrations in a physical system.
There are a number of approaches for achieving this end. One approach relies on altering the physical system in order to reduce any unwanted dynamics. For example, a robotic arm may be stiffened in order to reduce the amplitude of any residual vibrations, or the arm may be dampened so that residual vibrations quickly die out, or its mass be changed so that the resonant frequency of the arm is moved to a more favorable frequency. However, it is not always possible to alter the physical system. For example, the system may be so precisely designed as to be intolerant of the desired changes or it may just be physically impossible to alter the system, as is the case with a system which is inaccessible. Even if the system may be altered as desired, the alteration may come with a price--a more massive system, a larger actuator required to move the system or a more complex system, to name a few. Another approach relies on using a controller to actively reduce any unwanted dynamics. However, this approach also has its drawbacks. For example, most controllers rely on some sort of feedback from the unwanted dynamic and also on a good model of the system to be controlled, either of which may not always be available. In addition, controllers may be unacceptably complex, either in terms of the additional physical elements required to implement the controller or in terms of the time required for the controller to implement its control algorithm. In particular, fast real-time systems may be too fast for controllers to be an option.
A third approach, which is the approach considered by this invention, relies on altering the input to the system in order to reduce the unwanted dynamics. This approach does not rely on physical alterations to the system, good models of the system to be controlled, or complex real-time calculations. In related work, Singer, et. al. [Singer, Neil C.; Seering, Warren P. "Preshaping Command Inputs to Reduce System Vibration". ASME Journal of Dynamic Systems, Measurement, and Control. (March 1990) and Singer, et. al. U.S. Pat. No. 4,916,635, Apr. 10, 1990] showed that residual vibration can be significantly reduced by employing an Input Shaping.TM. method that uses a simple system model and requires very little computation. The model consists only of estimates of the system's natural frequency and damping ratio. Constraints on the system inputs result in zero residual vibration if the system model is exact. When modeling errors exist, the shaped inputs keep the residual vibration of the system at a low level that is acceptable for many applications. Extending the method to systems with more than one modeled resonant frequency is straightforward [Singer, Neil C. Residual Vibration Reduction in Computer Controlled Machines. Ph.D. Thesis, Massachusetts Institute of Technology. (February 1989)].
The shaping method works in real time by convolving a desired input with a sequence of impulses to produce the shaped input function that reduces residual vibration. The impulse sequence used in the convolution is called an input shaper. Selection of the number and type of impulses, the impulse amplitudes and their locations in time determine the amplitude and characteristics of the residual vibration. U.S. Pat. No. 4,916,635 discloses the basic concept of using input shapers, while the current invention discloses a variety of input shapers designed to achieve specific goals. Since the invention considers many different input shapers used for various purposes, the description of the preferred embodiment is subdivided into sections, with each section devoted to a specific class of input shapers.